Bennett Two Nodes one

Proved

D1Bound5.bennettTwoNodes_one

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result bennettTwoNodes_one in the proof of the bound five for Diophantine D(1) sets in imaginary quadratic integer rings. The formal statement specifies its hypotheses and conclusion; a mathematical prose description remains to be supplied.

Preamble

import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polynomial.Degree.Operations
import Mathlib.Combinatorics.Enumerative.Catalan.Basic
import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.PowerSeries.Binomial
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_BennettTwoIntegralEntries_Definitions

Formal statement

section
open Finset

namespace D1Bound5

variable {F : Type*} [Field F] [CharZero F]




@[simp] theorem _root_.D1Bound5.bennettTwoNodes_one (a b : F) : bennettTwoNodes a b 1 = b := by sorry
























end D1Bound5
end

Source

D1Bound5/BennettTwoIntegralEntries.lean, lines 15-15, SHA-256 07d63d84699ae294fc3d395f046972fa36aa179a18de306e5f612beceaaf5f1b. Project: https://github.com/tomislav-math/d1-bound5-lean

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